Fernando Santos' side dropped its first points in Group G with a goalless draw at home to Bosnia-Herzegovina last week, and finds itself in a three-way tie for top spot.
Slovakia's 2-1 victory over Latvia moved it alongside Greece, but Karagounis sees no reason why it cannot give itself some breathing space over its opponent.
"We wanted to win (in Bosnia), but even with the draw we remain at the top with the other two strongest teams in the group," the Fulham player told Era Sport.
"The match with Slovakia will be difficult but we will play to win. Our goal in every match is to win.
"We have confidence and know we can beat any opponent."
Slovakia's win over Latvia saw both midfielder Vladimir Weiss and defender Martin Skrtel leave the pitch with knee and head injuries, respectively.
However, the pair have returned to training and coach Michal Hipp is hopeful they will be able to play some part.
Bosnia-Herzegovina also sits alongside Slovakia and Greece on seven points but has the edge over its rivals on goal difference, and continues its qualifying campaign at home to Lithuania.
Victory would see Lithuania, which beat Liechtenstein 2-0 last week, move level with its opponent in a close-knit group.
However, Bosnia-Herzegovina midfielder Sejad Salihovic is determined not to let that happen.
He told www.nsfbih.ba: "We managed to do well in Greece.
"I think we also have a great chance at home of beating Lithuania, but we have to be careful. It will be a tough game we have to prepare for."
Latvia and Liechtenstein are both without a win in three attempts so far, but something will give when they meet in Riga.
The Latvians will have the advantage as host, but coach Aleksandrs Starkovs told www.lff.la: "While Liechtenstein are worse than us on paper, they are a hard nut to crack.
"They are an uncompromising, disciplined team. We are preparing very seriously for this match."